Abstract
In this article, we show that, $Q:_A\frak{m}^t\subseteq\frak{m}^t$ for all integers $t$ > 0, and for all parameter ideals $Q\subseteq\frak{m}^{2t-1}$ in a one-dimensional Cohen-Macaulay local ring $(A,\frak{m})$ provided that $A$ is not a regular local ring. The assertion obtained by Wang can be extended to one-dimensional (hence, arbitrary dimensional) local rings after some mild modifications. We refer to these quotient ideals $I = Q:_A\frak{m}^t$, $t$-th quasi-socle ideals of $Q$. Examples are explored.
Citation
Jun HORIUCHI. Hideto SAKURAI. "Wang's theorem for one-dimensional local rings." J. Math. Soc. Japan 66 (2) 641 - 646, April, 2014. https://doi.org/10.2969/jmsj/06620641
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